Property $(UW {\scriptstyle\Pi })$ and localized SVEP

Pietro Aiena,
Mohammed Kachad

Acta Sci. Math. (Szeged) 84:3-4(2018), 555-571
53/2016

Abstract. Property $(UW_{\Pi })$ for a bounded linear operator $T\in L(X)$ on a Banach space $X$ is a variant of Browder's theorem, and means that the points $\lambda $ of the approximate point spectrum for which $\lambda I-T$ is upper semi-Weyl are exactly the spectral points $\lambda $ such that $\lambda I-T$ is Drazin invertible. In this paper we investigate this property, and we give several characterizations of it by using typical tools from local spectral theory. We also relate this property with some other variants of Browder's theorem (or Weyl's theorem).

DOI: 10.14232/actasm-016-303-5

AMS Subject Classification
(1991): 47A53, 47A10, 47A11

Keyword(s):
property $(UW {\scriptstyle\Pi })$,
SVEP

Received September 26, 2016 and in final form May 15, 2018. (Registered under 53/2016.)